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We introduce the class of network right $*$-abundant semigroups. These are based on networks that extend the notion of a directed graph. This class properly contains the class of graph inverse semigroups. We investigate the structure of network right $*$-abundant semigroups. We show that two network right $*$-abundant semigroups are isomorphic if and only if the underlying networks are isomorphic.

The field of autonomous driving increasingly demands high-quality annotated video training data. In this paper, we propose Panacea+, a powerful and universally applicable framework for generating video data in driving scenes. Built upon the foundation of our previous work, Panacea, Panacea+ adopts a multi-view appearance noise prior mechanism and a super-resolution module for enhanced consistency and increased resolution. Extensive experiments show that the generated video samples from Panacea+ greatly benefit a wide range of tasks on different datasets, including 3D object tracking, 3D object detection, and lane detection tasks on the nuScenes and Argoverse 2 dataset. These results strongly prove Panacea+ to be a valuable data generation framework for autonomous driving., Comment: Project page: https://panacea-ad.github.io/. arXiv admin note: text overlap with arXiv:2311.16813

News captioning aims to describe an image with its news article body as input. It greatly relies on a set of detected named entities, including real-world people, organizations, and places. This paper exploits commonsense knowledge to understand named entities for news captioning. By ``understand'', we mean correlating the news content with common sense in the wild, which helps an agent to 1) distinguish semantically similar named entities and 2) describe named entities using words outside of training corpora. Our approach consists of three modules: (a) Filter Module aims to clarify the common sense concerning a named entity from two aspects: what does it mean? and what is it related to?, which divide the common sense into explanatory knowledge and relevant knowledge, respectively. (b) Distinguish Module aggregates explanatory knowledge from node-degree, dependency, and distinguish three aspects to distinguish semantically similar named entities. (c) Enrich Module attaches relevant knowledge to named entities to enrich the entity description by commonsense information (e.g., identity and social position). Finally, the probability distributions from both modules are integrated to generate the news captions. Extensive experiments on two challenging datasets (i.e., GoodNews and NYTimes) demonstrate the superiority of our method. Ablation studies and visualization further validate its effectiveness in understanding named entities.

We present MicroCinema, a straightforward yet effective framework for high-quality and coherent text-to-video generation. Unlike existing approaches that align text prompts with video directly, MicroCinema introduces a Divide-and-Conquer strategy which divides the text-to-video into a two-stage process: text-to-image generation and image\&text-to-video generation. This strategy offers two significant advantages. a) It allows us to take full advantage of the recent advances in text-to-image models, such as Stable Diffusion, Midjourney, and DALLE, to generate photorealistic and highly detailed images. b) Leveraging the generated image, the model can allocate less focus to fine-grained appearance details, prioritizing the efficient learning of motion dynamics. To implement this strategy effectively, we introduce two core designs. First, we propose the Appearance Injection Network, enhancing the preservation of the appearance of the given image. Second, we introduce the Appearance Noise Prior, a novel mechanism aimed at maintaining the capabilities of pre-trained 2D diffusion models. These design elements empower MicroCinema to generate high-quality videos with precise motion, guided by the provided text prompts. Extensive experiments demonstrate the superiority of the proposed framework. Concretely, MicroCinema achieves SOTA zero-shot FVD of 342.86 on UCF-101 and 377.40 on MSR-VTT. See https://wangyanhui666.github.io/MicroCinema.github.io/ for video samples., Comment: Project page: https://wangyanhui666.github.io/MicroCinema.github.io/

In this paper, we present CCEdit, a versatile generative video editing framework based on diffusion models. Our approach employs a novel trident network structure that separates structure and appearance control, ensuring precise and creative editing capabilities. Utilizing the foundational ControlNet architecture, we maintain the structural integrity of the video during editing. The incorporation of an additional appearance branch enables users to exert fine-grained control over the edited key frame. These two side branches seamlessly integrate into the main branch, which is constructed upon existing text-to-image (T2I) generation models, through learnable temporal layers. The versatility of our framework is demonstrated through a diverse range of choices in both structure representations and personalized T2I models, as well as the option to provide the edited key frame. To facilitate comprehensive evaluation, we introduce the BalanceCC benchmark dataset, comprising 100 videos and 4 target prompts for each video. Our extensive user studies compare CCEdit with eight state-of-the-art video editing methods. The outcomes demonstrate CCEdit's substantial superiority over all other methods.

This paper introduces the tensor representation of a network, here tensors are the primitive structures of the network. In view of tensor chains, two binary operations on tensor sets are defined: chain addition and reducing. Based on the reducing operation, the tensor chain representation of subnetworks of a network is given, and it is proved that all connected subnetworks of a network (here refers to the tensor chain generated by primitive structures) form a quasi-semilattice with respect to reducing, namely {\it network quasi-semilattices}. Here, quasi-semilattices refer to algebraic systems that are idempotent commutative and do not satisfy the association law. Then, we discuss the subalgebra structures of the network quasi-semilattice in terms of two equivalent relations $\sigma$ and $\delta$. $\delta$ is a congruence. Each $\delta$-class forms a semilattice with respect to reducing, that is, an idempotent commutative semigroup, and also each $\delta$-class has an order structure with the maximum element and minimum elements. Here, the minimum elements correspond to the spanning tree in graph theory. Finally, we discuss how three path algebras: graph inverse semigroups, Leavitt path algebra and Cuntz-Krieger graph $C^*$-algebra are constructed in terms of tensors with respect to chain-addition., Comment: 19 pages